Turbulence macroscale

The properties of the turbulence are different at the two extremes of the scale of turbulence. The largest eddies, known as the macroscale turbulence, contain most of the turbulent kinetic energy. Their motion is dominated by inertia and viscosity has little direct effect on them. In contrast, at the microscale of turbulence, the smallest eddies are dominated by viscous stresses, indeed viscosity completely smooths out the microscale turbulence. 

In the mesoscale model, setting Tf = 0 forces the fluid velocity seen by the particles to be equal to the mass-average fluid velocity. This would be appropriate, for example, for one-way coupling wherein the particles do not disturb the fluid. In general, fluctuations in the fluid generated by the presence of other particles or microscale turbulence could be modeled by adding a phase-space diffusion term for Vf, similar to those used for macroscale turbulence (Minier Peirano, 2001). The time scale Tf would then correspond to the dissipation time scale of the microscale turbulence. 

These relationships are valid for isolated bubbles moving under laminar flow conditions. In the case of turbulent flow, the effect of turbulent eddies impinging on the bubble surface is to increase the drag forces. This is typically accounted for by introducing an effective fluid viscosity (rather than the molecular viscosity of the continuous phase, yUf) defined as pi.eff = Pi + C pts, where ef is the turbulence-dissipation rate in the fluid phase and Cl is a constant that is usually taken equal to 0.02. This effective viscosity, which is used for the calculation of the bubble/particle Reynolds number (Bakker van den Akker, 1994), accounts for the turbulent reduction of slip due to the increased momentum transport around the bubble, which is in turn related to the ratio of bubble size and turbulence length scale. However, the reader is reminded that the mesoscale model does not include macroscale turbulence and, hence, using an effective viscosity that is based on the macroscale turbulence is not appropriate. 

The terms of the form (m/m/) are called the Reynolds stresses. The RANS equations do not consist of a closed set of equations (there are more unknowns than equations), so if the RANS equations are to be solved, the Reynolds stress terms must be modeled somehow. Typically, this modeling is based on experimental measurements. The application of models developed for macroscale flows to turbulent microchannel flows is dependent on the Reynolds stresses being similar for both cases. Recent experimental evidence suggests a strong similarity between turbulence statistics measured in turbulent microchannel flows and turbulence statistics measured in turbulent pipe and channel flows. Thus, the evidence suggests that turbulent models and codes developed to study macroscale turbulent pipe and channel flow should be applicable to the study of turbulent microchaimel flows. 

Velocity Fluctuations and Reynolds Stresses Li and Olsen [9, 10] were the first researchers to measure profiles of velocity fluctuations in turbulent microchannel flow. They measured streamwise and transverse velocity fluctuations and Reynolds shear stresses for a range of Reynolds numbers spanning the laminar through fully turbulent regime. They found good agreement between their measured fluctuations and Reynolds shear stresses and values reported for macroscale turbulent duct flow. 

Ten Cate et al. (2004) were able to learn from their DNS about the mutual effect of microscale (particle scale) events and phenomena at the macroscale the particle collisions are brought about by the turbulence, and the particles affect the turbulence. Energy spectra confirmed that the particles generate fluid motion at length scales of the order of the particle size. This results in a strong increase in the rate of energy dissipation at these length scales and in a decrease... 

Experimental data are available for large particles at Re greater than that required for wake shedding. Turbulence increases the rate of transfer at all Reynolds numbers. Early experimental work on cylinders (VI) disclosed an effect of turbulence scale with a particular scale being optimal, i.e., for a given turbulence intensity the Nusselt number achieved a maximum value for a certain ratio of scale to diameter. This led to speculation on the existence of a similar effect for spheres. However, more recent work (Rl, R2) has failed to support the existence of an optimal scale for either cylinders or spheres. A weak scale effect has been found for spheres (R2) amounting to less than a 2% increase in Nusselt number as the ratio of sphere diameter to turbulence macroscale increased from zero to five. There has also been some indication (M15, S21) that the spectral distribution of the turbulence affects the transfer rate, but additional data are required to confirm this. The major variable is the intensity of turbulence. Early experimental work has been reviewed by several authors (G3, G4, K3). 

In addition, the turbulent fluctuations set up a microscale type of shear rate. Microscale mixing tends to affect particles that are less than 100 /xm in size. The scaleup rules are quite different for macroscale controlled process in comparison to microscale. For example, in microscale processes, the major variables are the power per unit volume dissipated in various points in the vessel and the total average power per unit volume. In macroscale mixing, the energy level is important, as well as the geometry and design of the impeller blades and the way that they set up macroscale shear rates in the tank. 

In turbulence theory, this is also known as the concentration macroscale, which plays an important role in the interpretation of micromixing phenomena. 

Turbulence is needed to provide adequate contact between the waste and oxygen across the combustion chamber (macroscale mixing). Nevertheless, in the final stage, combustion at the molecular level occurs via diffusion or premixed flames, although the former is the dominant mode of waste destruction in practical systems. 

The flow of the continuous phase is considered to be initiated by a balance between the interfacial particle-fluid coupling - and wall friction forces, whereas the fluid phase turbulence damps the macroscale dynamics of the bubble swarms smoothing the velocity - and volume fraction fields. Temporal instabilities induced by the fluid inertia terms create non-homogeneities in the force balances. Unfortunately, proper modeling of turbulence is still one of the main open questions in gas-liquid bubbly flows, and this flow property may significantly affect both the stresses and the bubble dispersion [141]. 

Figure 22 shows the flow pattern when there is sufficient power and low enough viscosity for turbulence to form. Now a velocity probe must be used that can pick up the high frequency response of these turbulent flow patterns, and a chart as shown in Fig. 23 is typical. The shear rate between the small scale velocity fluctuations is called microscale shear rate, while the shear rates between the average velocity at this point are called the macroscale rates. These macroscale shear rates still have the same general form and are determined the same way as shown in Fig. 21. 

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